Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models
Takashi Hayakawa and Satoshi Asai
基于高斯过程的分层贝叶斯模型被认为对描述现实世界数据中变量之间的复杂非线性统计依赖性很有用。 然而,有效的蒙特卡洛算法与这些模型的推理尚未建立,除了几个简单的案例。 在这项研究中,我们表明,与现有程序库实现的缓慢推理相比,Riemannian-manielmanian Monte Carlo(RMHMC)的性能可以通过根据模型结构优化计算顺序并动态编程特征分解来大幅提高。 当使用基于幼稚自动区分器的现有库时,无法实现这种改进。 我们在数值上证明,RMHMC有效地从后验样本,允许计算模型证据,在模拟数据的贝叶斯逻辑回归,以及使用几个贝叶斯多内核模型估计美国国家医疗支出数据的倾向函数。 这些结果为实施有效的蒙特卡洛算法与高斯流程分析真实数据奠定了基础,并强调了开发可定制的库集的必要性,该库集允许用户结合动态编程对象,并根据模型结构精细地优化自动区分模式。
Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these models have not yet been established, except for several simple cases. In this study, we show that, compared with the slow inference achieved with existing program libraries, the performance of Riemannian-manifold Hamiltonian Monte Carlo (RMHMC) can be drastic...
